462 citations · 748 across the 21 of their papers we have counts for
22 papers
How to Compare Copula Forecasts?
Tobias Fissler, Yannick Hoga
This paper lays out a principled approach to compare copula forecasts via strictly consistent scores. We first establish the negative result that, in general, copulas fail to be el…
Elicitability and identifiability of tail risk measures
Tobias Fissler, Fangda Liu, Ruodu Wang +1
Tail risk measures are fully determined by the distribution of the underlying loss beyond its quantile at a certain level, with Value-at-Risk, Expected Shortfall and Range Value-at…
Generalised Covariances and Correlations
Tobias Fissler, Marc-Oliver Pohle
The covariance of two random variables measures the average joint deviations from their respective means. We generalise this well-known measure by replacing the means with other st…
Characterizing M-estimators
Timo Dimitriadis, Tobias Fissler, Johanna Ziegel
We characterize the full classes of M-estimators for semiparametric models of general functionals by formally connecting the theory of consistent loss functions from forecast evalu…
Osband's Principle for Identification Functions
Timo Dimitriadis, Tobias Fissler, Johanna Ziegel
Given a statistical functional of interest such as the mean or median, a (strict) identification function is zero in expectation at (and only at) the true functional value. Identif…
Measurability of functionals and of ideal point forecasts
Tobias Fissler, Hajo Holzmann
The ideal probabilistic forecast for a random variable based on an information set is the conditional distribution of given . In the context of p…
Sensitivity Measures Based on Scoring Functions
Tobias Fissler, Silvana M. Pesenti
We propose a holistic framework for constructing sensitivity measures for any elicitable functional of a response variable. The sensitivity measures, termed score-based sensiti…
Model Comparison and Calibration Assessment: User Guide for Consistent Scoring Functions in Machine Learning and Actuarial Practice
Tobias Fissler, Christian Lorentzen, Michael Mayer
One of the main tasks of actuaries and data scientists is to build good predictive models for certain phenomena such as the claim size or the number of claims in insurance. These m…
Deep Quantile and Deep Composite Model Regression
Tobias Fissler, Michael Merz, Mario V. Wüthrich
A main difficulty in actuarial claim size modeling is that there is no simple off-the-shelf distribution that simultaneously provides a good distributional model for the main body…
Is the mode elicitable relative to unimodal distributions?
Claudio Heinrich-Mertsching, Tobias Fissler
Statistical functionals are called elicitable if there exists a loss or scoring function under which the functional is the optimal point forecast in expectation. While the mean and…
Backtesting Systemic Risk Forecasts using Multi-Objective Elicitability
Tobias Fissler, Yannick Hoga
Systemic risk measures such as CoVaR, CoES and MES are widely-used in finance, macroeconomics and by regulatory bodies. Despite their importance, we show that they fail to be elici…
The Efficiency Gap
Timo Dimitriadis, Tobias Fissler, Johanna Ziegel
Parameter estimation via M- and Z-estimation is equally powerful in semiparametric models for one-dimensional functionals due to a one-to-one relation between corresponding loss an…
Forecast Evaluation of Quantiles, Prediction Intervals, and other Set-Valued Functionals
Tobias Fissler, Rafael Frongillo, Jana Hlavinová +1
We introduce a theoretical framework of elicitability and identifiability of set-valued functionals, such as quantiles, prediction intervals, and systemic risk measures. A function…
Elicitability and Identifiability of Systemic Risk Measures
Tobias Fissler, Jana Hlavinová, Birgit Rudloff
Identification and scoring functions are statistical tools to assess the calibration and the relative performance of risk measure estimates, e.g., in backtesting. A risk measures i…
Evaluating Range Value at Risk Forecasts
Tobias Fissler, Johanna F. Ziegel
The debate of what quantitative risk measure to choose in practice has mainly focused on the dichotomy between Value at Risk (VaR) -- a quantile -- and Expected Shortfall (ES) -- a…
Supplement to "Erratum: Higher Order Elicitability and Osband's Principle"
Tobias Fissler, Johanna F. Ziegel
This note corrects conditions in Proposition 3.4 and Theorem 5.2(ii) and comments on imprecisions in Propositions 4.2 and 4.4 in Fissler and Ziegel (2016).
Order-Sensitivity and Equivariance of Scoring Functions
Tobias Fissler, Johanna F. Ziegel
The relative performance of competing point forecasts is usually measured in terms of loss or scoring functions. It is widely accepted that these scoring function should be strictl…
A new quantitative central limit theorem on the Wiener space with applications to Gaussian processes
Tobias Fissler, Christoph Thaele
Quantitative limit theorems for non-linear functionals on the Wiener space are considered. Given the possibly infinite sequence of kernels of the chaos decomposition of such a func…
Expected Shortfall is jointly elicitable with Value at Risk - Implications for backtesting
Tobias Fissler, Johanna F. Ziegel, Tilmann Gneiting
In this note, we comment on the relevance of elicitability for backtesting risk measure estimates. In particular, we propose the use of Diebold-Mariano tests, and show how they can…
Higher order elicitability and Osband's principle
Tobias Fissler, Johanna F. Ziegel
A statistical functional, such as the mean or the median, is called elicitable if there is a scoring function or loss function such that the correct forecast of the functional is t…
A four moments theorem for Gamma limits on a Poisson chaos
Tobias Fissler, Christoph Thaele
This paper deals with sequences of random variables belonging to a fixed chaos of order generated by a Poisson random measure on a Polish space. The problem is investigated whe…
Testing the maximal rank of the volatility process for continuous diffusions observed with noise
Tobias Fissler, Mark Podolskij
In this paper, we present a test for the maximal rank of the volatility process in continuous diffusion models observed with noise. Such models are typically applied in mathematica…